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Number of electron states in 1Bz

  1. Sep 20, 2007 #1

    malawi_glenn

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    1. The problem statement, all variables and given/known data

    How many electron states are there in the irreducable part of 1BZ (one irreducable part is 1/48 of 1BZ).


    2. Relevant equations

    Volume of 1Bz:
    [tex] \Omega = \dfrac{(2 \pi)^3}{V} [/tex]

    Volume of ordinary cell:
    [tex] V = a^3 [/tex]

    Density of states, I assume that the temperature is so low that fermi-dirac function does not play big part, hence max energy = fermi energy.

    [tex] D(\epsilon ) = \dfrac{V}{2 \pi ^2} \left( \dfrac{2m}{\hbar ^2} \right)^{3/2} \sqrt{\epsilon } [/tex]

    3. The attempt at a solution

    total number of states:
    [tex] \int_0^{\epsilon _{F}} D(\epsilon ) d \epsilon [/tex]

    just gives me N = N

    :S

    What do I do wrong? My plan was first to calculate the number of states i ordinary space, then convert into reciprocal space...
     
  2. jcsd
  3. Sep 20, 2007 #2

    malawi_glenn

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    Never mind, I will ask my teacher tomorrow.
     
  4. Sep 21, 2007 #3

    malawi_glenn

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    First Brillouin zone, A very common short notation for it...

    And I realized that there is N number of k-values in 1 BZ, so that there is N/24 in the irreducible 1 BZ, since there is two electron states per k-value due to pauli principle.
     
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